Question: Simplify the following expression: $\dfrac{54a^4}{30a^2}$ You can assume $a \neq 0$.
$ \dfrac{54a^4}{30a^2} = \dfrac{54}{30} \cdot \dfrac{a^4}{a^2} $ To simplify $\frac{54}{30}$ , find the greatest common factor (GCD) of $54$ and $30$ $54 = 2 \cdot 3 \cdot 3 \cdot 3$ $30 = 2 \cdot 3 \cdot 5$ $ \mbox{GCD}(54, 30) = 2 \cdot 3 = 6 $ $ \dfrac{54}{30} \cdot \dfrac{a^4}{a^2} = \dfrac{6 \cdot 9}{6 \cdot 5} \cdot \dfrac{a^4}{a^2} $ $\phantom{ \dfrac{54}{30} \cdot \dfrac{4}{2}} = \dfrac{9}{5} \cdot \dfrac{a^4}{a^2} $ $ \dfrac{a^4}{a^2} = \dfrac{a \cdot a \cdot a \cdot a}{a \cdot a} = a^2 $ $ \dfrac{9}{5} \cdot a^2 = \dfrac{9a^2}{5} $